st: Interpretation of Two-sample t test with equal variances?

[Gwinyai Masukume <parturitions@gmail.com>]

Dear Stata list,

I would like to double check the interpretation and appropriateness of
the following statistical test I performed.
My alternate hypothesis is that, “There is a difference in the baby’s
mode of delivery depending on maternal age” And the null hypothesis is
that, “There is no difference in the baby’s mode of delivery depending
on maternal age”
Looking at the output – “Ha: diff != 0, Pr(|T| > |t|) = 0.4861”, I
fail to reject the null hypothesis and conclude that, “There is no
difference in the baby’s mode of delivery depending on maternal age”

Is this a sound and appropriate interpretation?

. *** Doing a T-test
. ttest age, by(mode_delivery)

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
 Vaginal |     166    28.83072    .4696729    6.051313    27.90338    29.75807
C/sectio |      84    29.39524    .6579862    6.030543    28.08653    30.70395
---------+--------------------------------------------------------------------
combined |     250     29.0204    .3818851    6.038134    28.26826    29.77254
---------+--------------------------------------------------------------------
    diff |           -.5645152    .8093331               -2.158558    1.029528
------------------------------------------------------------------------------
    diff = mean(Vaginal) - mean(C/sectio)                         t =  -0.6975
Ho: diff = 0                                     degrees of freedom =      248

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.2431         Pr(|T| > |t|) = 0.4861          Pr(T > t) = 0.7569

With kind regards,
Gwinyai

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